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Finding the Third Proportional to 415.25 and 582.25

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Solution

The third proportional to 415.25 and 582.25 is: 816.41

Step by Step Solution

  1. Step 1: Write the proportion equation
    415.25 : 582.25 = 582.25 : x
  2. Step 2: Convert to fraction form
    415.25/582.25 = 582.25/x
  3. Step 3: Cross multiply
    415.25x = 582.25 × 582.25
  4. Step 4: Simplify right side
    415.25x = 339,015.06
  5. Step 5: Solve for x
    x = 339,015.06/415.25
  6. Step 6: Final answer
    x = 816.41

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Why These Related Problems?

These problems maintain the same ratio (1.40) or explore similar proportional relationships. Practicing with related ratios helps build understanding of proportional relationships.